Federated Learning for Smart Grids: Mathematical Formulation and Algorithms

The rapid digitalization of power systems has resulted in the widespread deployment of sensing, communication, and automation technologies across smart grids. These systems generate massive volumes of distributed data that can be exploited using machine learning techniques for forecasting, monitoring, and control. However, conventional centralized learning approaches are increasingly constrained by privacy regulations, communication overhead, and cyber-security risks. Federated learning (FL) has emerged as a decentralized machine learning paradigm that enables collaborative model training without transferring raw data. This paper presents a comprehensive IEEE-compliant formulation of federated learning for smart grid applications. Mathematical modeling, federated optimization algorithms, privacy-preserving aggregation mechanisms, and performance evaluation metrics are systematically discussed. The suitability of federated learning for load forecasting, fault diagnosis, renewable integration, and electric vehicle management is highlighted. Challenges and future research directions for federated intelligence in power systems are also outlined.